In reply to Dandan:
> I'd imagine it would be fine, if it's really that cheap and you are that concerned, then just glue it up into 3x4's, it'll be ridiculously sturdy then.
You are correct but it will only be twice as sturdy.
Build it in 3*2.
Then if you are unhappy with the flex, glue and screw 2*3 onto the back to make 3*5 T section.
Over twice as stiff again and the same amount of timber used. ( Stiffness proportional to B * D * D ) HTH.